Dutch paints and chemicals maker Akzo Nobel NV said Thursday it had rejected a €20.9 billion ($22.1 billion) offer from U.S. peer PPG Industries Inc., setting up a trans-Atlantic standoff between two long-lived industrial giants amid a wave of consolidation in the sector.

Amsterdam-based Akzo also said Thursday that it is exploring selling off its special-chemicals division—a disclosure, it said, prompted by PPG’s unsolicited offer....